It is given by the ratio of pressure applied to the corresponding relative decrease in the volume of the material. Mathematically, it is represented as follows: B = Δ P / ( Δ V / V ) Where: B : Bulk modulus Δ P : change of the pressure or force applied per unit area on the material Δ V : change of the volume of the material due to the compression V : Initial volume of the material.

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A uniform rod of length $L$ has a mass per unit length $λ$ and area of cross-section $A .$ If the Young's modulus of the rod is $Y$ . Then elongation in the rod due to its own weight is

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Important Questions on Mechanical Properties of Solids

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Gamma Question Bank for Medical Physics>Chapter 9 - Mechanical Properties of Solids>Assignment>Q 8

A solid sphere of radius

R

made of a material of bulk modulus

B

surrounded by a liquid in a cylindrical container. A massless piston of area

A

floats on the surface of the liquid. Find the fractional decrease in the radius of the sphere

(\frac{Δ R}{R})

when a mass

M

is placed on the piston to compress the liquid

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Gamma Question Bank for Medical Physics>Chapter 9 - Mechanical Properties of Solids>Assignment>Q 9

A sphere contracts in volume by

0.01 %

when taken to the bottom of sea

1 km

deep. Find Bulk modulus of the material of sphere

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Gamma Question Bank for Medical Physics>Chapter 9 - Mechanical Properties of Solids>Assignment>Q 10

A solid cube of copper of edge

10 cm

subjected to a hydraulic pressure of

7 \times 10^{6} Pa

. If Bulk modulus of copper is

140 GPa

, then contraction in its volume will be

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Gamma Question Bank for Medical Physics>Chapter 9 - Mechanical Properties of Solids>Assignment>Q 11

Three bars having length

l, 2 l

and

3 l

and area of cross-section

A, 2 A

and

3 A

are joined rigidly end to end. Compound rod is subjected to a stretching force

F

. The increase in length of rod is (Young's modulus of material is

Y

and bars are massless)

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Gamma Question Bank for Medical Physics>Chapter 9 - Mechanical Properties of Solids>Assignment>Q 12

An ideal gas has adiabatic exponent $\gamma$. It contracts according to the law

P V = α

, where

α

is a positive constant. For this process, the Bulk modulus of the gas is

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Gamma Question Bank for Medical Physics>Chapter 9 - Mechanical Properties of Solids>Assignment>Q 13

Two wire

A

and

B

are stretched by same force. If, for

A

and

B, Y_{A} : Y_{B} = 1 : 2, r_{A} : r_{B} = 3 : 1

and

I_{A} : I_{B} = 4 : 1

, then ratio of their extension

(\frac{Δ I_{A}}{Δ I_{B}})

will be

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Gamma Question Bank for Medical Physics>Chapter 9 - Mechanical Properties of Solids>Assignment>Q 14

A bar is subjected to axial forces as shown. If $E$ is the modulus of elasticity of the bar and, $A$ is its cross-section area. Its elongation will be

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Gamma Question Bank for Medical Physics>Chapter 9 - Mechanical Properties of Solids>Assignment>Q 15

A metal ring of initial radius

r

and cross-sectional area

A

is fitted onto a wooden disc of radius

R > r

. If Young's modulus of metal is

Y

then tension in the ring is

A uniform rod of length L has a mass per unit length λ and area of cross-section A. If the Young's modulus of the rod is Y. Then elongation in the rod due to its own weight is

Important Questions on Mechanical Properties of Solids

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A uniform rod of length $L$ has a mass per unit length $λ$ and area of cross-section $A .$ If the Young's modulus of the rod is $Y$ . Then elongation in the rod due to its own weight is